SOLUTION: Police departments use exams as part of their promotion process and officers have to score higher than 80% of those taking the test to be considered for promotion. Officer #1 recei

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Question 854621: Police departments use exams as part of their promotion process and officers have to score higher than 80% of those taking the test to be considered for promotion. Officer #1 receives a raw score of 76 and Officer #2 receives a raw score of 68. The mean of all the exam scores is 62 with a standard deviation of 11.
1) Calculate the z score for Officer #1. Will he be promoted?
2) Calculate the z score for Officer #2. Will she be promoted?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
Officer 1 gets 76
Officer 2 gets 68
mean of all scores is 62 with standard deviation of 11.

z-score = (x-m) / s

x = the raw score of the officer taking the test.
m = the mean of all scores.
s = the standard deviation of all scores.

z-score for Officer 1 is (76-62)/11 = 14/11 = 1.28
z-score for Officer 2 is (68-62)/11 = 6/11 = .55

probability of getting a z-score less than 1.28 is .9.
probability of getting a z-score less than .71.

Officer 1 will get promoted.
Officer 2 will not.

you look up the z-scores in the z-score table and the table tells you the probability of getting a score less than that.

i used the ti-84 calculator, but you can get similar results with the following table:

http://lilt.ilstu.edu/dasacke/eco148/ztable.htm

for example:

i looked for a z-score of 1.28

the left column will show me the row where 1.2 is and the 10th column for that row will give me the area under the distribution curve to the left of the z-score of 1.28 which is equal to 1.2 from the first column plus .08 from the 10th column to get 1.28.

the area shown there is .8997 which is rounded to .9.